Question

como resolver essa fraçao geratriz 2,305757

Answer 1

2,305757... = 2,30 + 0,0057 + 0,000057 + ...

P.G. = (0,0057; 0,000057;...)

$q= \frac{a_2}{a_1} \\ \\ q= \frac{0,000057}{0,0057} \\ \\ q= \frac{57}{5700} \\ \\ q= \frac{1}{100}$



$S_{n \to \infty}= \frac{a_1}{1-q} \\ \\ S_n= \frac{0,0057}{1- \frac{1}{100} } \\ \\S_n= \frac{0,0057}{ \frac{99}{100} } \\ \\ S_n=0,0057* \frac{100}{99} \\ \\ S_n= \frac{0,57}{99} \\ \\ S_n= \frac{ \frac{57}{100} }{99} \\ \\ S_n= \frac{57}{9900} \\ \\ S_n= \frac{19}{3300}$


2,305757... = 2,30 + 0,0057 + 0,000057 + ...

2,305757... = 2,30 + 19/3300


$2,30+ \frac{19}{3300}= \\ \\ \frac{23}{10}+ \frac{19}{3300}= \\ \\ \frac{7590+19}{3300}= \\ \\ \frac{7609}{3300}$



$0,305757...= \frac{7609}{3300}$